Question: Rewrite as a simplified fraction. ${0.7\overline{62} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 762.6262...\\ 10x &= 7.6262...\end{align*}}$ Subtracting the two equations, we have: ${990x = 755}$ ${x = \dfrac{755}{990}} $ ${x = \dfrac{151}{198}} $